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Convergence analysis of wavelet schemes for convection-reaction equations under minimal regularity assumptions. (English) Zbl 1091.65096

The initial value problem for the multidimensional linear convection-reaction equation is considered. For a numerical solution of this problem the authors propose one of characteristic methods – the Eulerian-Lagrangian localized adjoint method. Then error estimates for the numerical schemes are formulated and proved. The estimates are obtained under some minimal regularity assumptions in the L-norm and in a Besov space. Numerical experiments illustrate the theoretical results.

MSC:

65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
35L15 Initial value problems for second-order hyperbolic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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